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arXiv · 1506.05743

"Irregularization" of Systems of Conservation Laws

Hunter Swan·Woosong Choi·Stefanos Papanikolaou·Matthew Bierbaum·Yong S. Chen·James P. Sethna
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Abstract

We explore new ways of regulating defect behavior in systems of conservation laws. Contrary to usual regularization schemes (such as a vanishing viscosity limit), which attempt to control defects by making them smoother, our schemes result in defects which are \textit{more singular}, and we thus refer to such schemes as "irregularizations". In particular, we seek to produce \textit{delta shock} defects which satisfy a condition of \textit{stationarity}. We are motivated to pursue such exotic defects by a physical example arising from dislocation dynamics in materials physics, which we describe.

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Hunter Swan, Woosong Choi, Stefanos Papanikolaou, Matthew Bierbaum, Yong S. Chen, James P. Sethna. 2015-06-18. "Irregularization" of Systems of Conservation Laws. https://arxiv.org/abs/1506.05743

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